They were completely yellow before, so I wet-sanded up to 2000 grit sandpaper and then polished them with Meguiar's plastic polish - so they look great now, however, the damn mechanic doing the inspection says there are still too cloudy. Nonsense!

Therein lies your problem. You should use 3M rubbing compound between the 2000 grit sanding and the plastic polish. On the first DIY to which I linked, the guy was able to get away without using rubbing compound. For whatever reason, it worked. In your case it didn't. I had the exact same lights as you and got awesome results using 3M. It looks like you still have some 2000 grit scratches on there. Hit it with the rubbing compound first, then polish again. Trust me on this it'll look a lot better.